CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

The perimeter is given of right triangle is 24 cm if its hypotenuse is 10 cm find its area


Solution

Given the perimeter = 24 cm

The hypotenuse = 10

Then we know that the perimeter of the triangle is the sum of all three sides:

Let the sides be x , y , and the hypotenuse = 10

==> x + y + 10 = 24

==> x + y = 14

==> x = 14 - y  ............(1)

Also we know that:

 x^2 + y^2 = 10^2

==> x^2 + y^2 = 100 .............(2)

...

Given the perimeter = 24 cm

The hypotenuse = 10

Then we know that the perimeter of the triangle is the sum of all three sides:

Let the sides be x , y , and the hypotenuse = 10

==> x + y + 10 = 24

==> x + y = 14

==> x = 14 - y  ............(1)

Also we know that:

 x^2 + y^2 = 10^2

==> x^2 + y^2 = 100 .............(2)

now we will substitute (1) in (2):

==> (14-y)^2 + y^2 = 100

==> 196 - 28y + y^2 + y^2 = 100

==?> 2y^2 - 28y + 196 = 100

==> 2y^2 - 28y + 96 = 0

Let us divide by 2:

==> y^2 -14y + 48 = 0

==> we will factor:

==> ( y - 8 ) ( y- 6)

==> y1= 8 ==> x1= 6

==> y2 = 6 ==> x2= 8

But given : x> y

==> x = 8   and y = 6

flag
 Suggest corrections
thumbs-up
 
0 Upvotes


Similar questions
QuestionImage
QuestionImage
View More...



footer-image